Global Well-posedness for the Focusing Cubic NLS on the Product Space $\mathbb{R} \times \mathbb{T}^3$

Source abstract

In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schrödinger equation on the product space $\mathbb{R} \times \mathbb{T}^3$ with initial data below the threshold that arises from the the ground state in the Euclidean setting. The defocusing analogue was discussed and proved in Ionescu and Pausader [ Comm. Math. Phys., 312 (2012), pp. 781--831].